Some versions of the sixth Taylor Swift album come complete with a sleeve note, penned by the 27-year-old singer-songwriter. It opens with some general thoughts on social media: the rumours that abound on it are not always true, the images people present of themselves there not always reflective of reality. Then it moves on to the pressures of life in the glare of the media’s spotlight – “My heartbreaks have been used as entertainment” – and offers a swift rebuke to those who might attempt to interpret Swift’s songs as being about her personal life. “When this album comes out, gossip blogs will scour the lyrics for the men they can attribute to each song … there will be slideshows of photos backing up each incorrect theory.”

It is at this point that even the most devoted Taylor Swift fan might find the words “Oh, come off it” involuntarily springing from their lips. She has a very good point about the wearying way work by female singer-songwriters is invariably interpreted as autobiographical, while that of their male counterparts is not. (“I feel like sometimes, when people describe music as confessional, it’s a term that they relegate to female artists,” is how St Vincent’s Annie Clark put it a couple of years ago.) However, it is hard to think of another pop star who’s proved so brilliant at manipulating the media through their music, at exploiting its prurient obsession with the minutiae of celebrities’ lives – their romances, their feuds, real or imagined. With respect, it feels a bit rich to start complaining about people sifting through your lyrics for clues to who they are about when you’ve trailed your new album with Look What You Made Me Do, a song and video so stuffed with knowing references to your private life that fans felt impelled to compile guides to every oblique allusion as if it was The Waste Land, rather than a three-minute pop song with a chorus pinched from I’m Too Sexy by Right Said Fred.

Perhaps it is an elaborate double bluff: if those allusions are what you want, as much as it pains me, that’s what I’ll give you. Certainly, if your thing is songs that leave you wondering who or what they might be referencing, then Reputation is very much the album for you: “Let the games begin,” announces opener … Ready for It?, as if the whole thing is a puzzle waiting to be solved. From its title down, Reputation is an album frequently obsessed with gossip – “All the liars are calling me one”, “A circus ain’t a love story” and “If he drops my name then I owe him nothing” – along with the machinations of nameless foes. “I got some big enemies,” offers End Game, while This Is Why We Can’t Have Nice Things spends three and a half minutes with its mouth pursed into a cat’s bum of disapproval, dressing down a former friend, with many references to the exquisite life of champagne-swilling said friend will now be excluded from as punishment for incurring Swift’s wrath. Whoever the subject, its moneyed bitterness is a little unedifying to listen to, like Morrissey after taking delivery of a black Amex card.

These lyrics are frequently set to music that sees Swift cutting her last ties with her Nashville roots in favour of the blare and honk of EDM-influenced pop. At their best, these songs have a fizzing, pugilistic energy that recalls Britney Spears’ brilliant, mid-breakdown, screw-you-all 2007 album Blackout (in another reference to Spears, the brilliant chorus of Don’t Blame Me features a chord progression that recalls Hit Me, Baby, One More Time). At their least appealing, they’re still decent pop songs, but they feel generic: they could be by Rihanna or Rita Ora. For all her protestations, you’re struck by the sense that a strain of songwriting beginning with the withering, chatter-inducing conundrum of Carly Simon’s You’re So Vain – a song that Swift invited Simon to sing with her on stage during her 2013 tour – is reaching its terminal phase here, where the song is less important than the lyrics’ ability to create what Swift refers to as “drama”.

Her lyrics are, well, lyrical: ‘You should think about the consequences of your magnetic field being a little too strong’

If that were all Reputation had to offer lyrically, it would be a disappointment – but it isn’t. Swift is a smart cookie. She’s smart enough to write lyrics far better and wittier than the average pop fare, inverting the cliche of the love ’em and leave ’em Romeo – “I’ll carve your name on my bedpost,” she snarls – and admitting defeat when her chat-up lines fail with a sigh of “I guess I’ll stumble home to my cats – alone”. And she’s certainly too smart to put all her eggs in one basket. At the heart of Reputation lies a sequence of songs that chart the rise, fall and fallout of a fleeting relationship and offer a masterclass in pop songwriting along the way. Gorgeous, Getaway Car and King of My Heart are filled with fantastic melodies – the tune of Gorgeous has a lovely, melancholy Abba-like quality – and lyrics that sound, well, lyrical: “You should think about the consequence of your magnetic field being a little too strong.” Meanwhile, Dancing With Our Hands Tied fruitfully returns to the AOR-inspired sound of 1989, while the closing New Year’s Day proves an exception to the general rule that the piano ballad is the low point of any pop album, and exposes musical roots that Reputation conceals elsewhere: you don’t get anywhere on Music Row unless you know how to knock out a romantic weepie that hits them where it hurts.

It provides the conclusion to an album that feels like a conclusion in itself. It stretches one aspect of Swift’s songwriting to its elastic limit: Look What You Made Me Do and This Is Why We Can’t Have Nice Things feel like the end of the line for the kind of songs that provoke fans to start throwing hashtags around and pronouncing themselves Team Taylor. But Reputation also suggests that doesn’t matter: as the sleeve notes point out and the songs confirm, there’s more to Taylor Swift than dropping hints and creating drama.